I use bleach spray occasionally, if I am in a hurry. I have never had a problem with it being "reactivated" so I would say your most likely safe.
Most of the time I use real bleach mixed half and half with water in a bucket, then rinse the cage with plain water, and dry. I only use fake trees, plants, hides, etc. and I wash them with plain dish soap. If you happen to use any real wood, you could bake them in the oven at 350 degrees for about an hour, that is the only way to kill bacteria on real wood. You are better off not using real wood though, they hold bacteria, and if you get mites, forget trying to treat it.